Factor 2x^2+7x+3
Factor polynomials completely: trinomials, difference of squares, sum/difference of cubes.
To factor 2x^2+7x+3 with a leading coefficient of 2, use the AC method (factoring by grouping).
2x2+7x+3
Identify the coefficients: a = 2, b = 7, c = 3
Since the leading coefficient is 2 (not 1), use the AC method:
Multiply the leading coefficient (a) by the constant term (c):
a × c = 2 × 3 = 6
Find two numbers that multiply to 6 and add to 7:
6 × 1 = 6, 6 + 1 = 7 → use 6 and 1
Rewrite +7x as +6x and +x:
2x2 + 6x + x + 3
(2x2 + 6x) + (x + 3)
Factor the GCF from each group:
(2x2 + 6x) = 2x(x + 3)
(x + 3) is already in the form 1 · (common factor)
Both groups share the same binomial factor — pull it out:
= (x + 3)(2x + 1)
(x + 3)(2x + 1)
How to factor 2x^2+7x+3
To factor 2x^2+7x+3, identify the type of polynomial and apply the appropriate technique. The factored form is (x + 3)(2x + 1).
This is a polynomial factoring problem — we break a polynomial into a product of simpler expressions. Common methods include GCF extraction, difference of squares, and trinomial factoring.
Frequently asked questions
What is the answer to 2x^2+7x+3?
The answer is (x + 3)(2x + 1).
What method is used?
identifying the polynomial type and applying the matching technique — GCF, trinomial factoring, difference of squares, or special cube formulas.